Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae

DOI10.1007/BF02108334zbMath0842.58072MaRDI QIDQ1894886

Denis V. Kosygin, Yakov G. Sinai, Pavel M. Bleher

Publication date: 26 July 1995

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

eigenvaluesLaplace operatorWeyl asymptotic formulaLiouville torus

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (4)

Spectrum of the Laplace operator on closed surfaces ⋮ Circle problem and the spectrum of the Laplace operator on closed 2-manifolds ⋮ Riemannian manifolds with uniformly bounded eigenfunctions ⋮ Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems

Cites Work

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• Chaos in classical and quantum mechanics
• On the distribution of the number of lattice points inside a family of convex ovals
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems
• Topological classification of integrable geodesic flows on orientable two-dimensional Riemannian manifolds with additional integral depending on momenta linearly or quadratically
• Distribution of energy levels of a quantum free particle on a surface of revolution
• Semiclassical quantization rules near separatrices
• Distribution of the error term for the number of lattice points inside a shifted circle
• The spectral function of an elliptic operator
• Fourier integral operators. I
• Scattering Theory for Automorphic Functions. (AM-87)
• Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
• Chebyshev's Bias
• The distribution and moments of the error term in the Dirichlet divisor problem
• Lectures on spectral theory of elliptic operators

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